Question

Find the slope of a line perpendicular to the line that passes through the points (7.10) and (13,8).

Answer 1

Perpendicular Lines

Suppose we know the slope of one line is m1 and we want to calculate the slope m2 of another line that is perpendicular to the first line.

The slopes are related by the formula:

`m_1\cdot m_2=-1`

Solving for m2:

`m_2=-(1)/(m_1)`

We are given the points (7, 10) and (13, 8) through which a given line passes. Calculate the slope of this line:

`\begin{gathered} m_1=(8-10)/(13-7) \\ \text{Operating:} \\ m_1=(-2)/(6) \\ m_1=-(1)/(3) \end{gathered}`

Now compute the slope m2:

`m_2=-(1)/(-(1)/(3))`

To divide by a fraction, we multiply by its reciprocal:

`\begin{gathered} m_2=-1\cdot(-(3)/(1)) \\ m_2=3 \end{gathered}`

The slope of the line is 3